Pattern and Geometry Based Architecture

After attending a lecture by SD on Masonry Temple Architecture, I thought I would dig this post out again and have another look at the method and calculations that had to occur to form the structure. Geometry is cool! Now I want to find more of these patterns and try them out...

So this is what I started out with...a pattern in a book.

Next, how does this pattern work, geometrically speaking? I found everything could be derived from a ratio or as a proportion of something else.

Now that I've figured out how the pattern works, how does the overlay work?

Now I have an underlying pattern with an overlay from which to start projecting three dimensionally.

If the pattern is rotated so that there are two, then I can make a vault.

From the instructions in the book, I work out how to calculate the shape of the projection in the third dimension.

Again, this is formed by lines with a geometric relationship, that goes like this:
AB = width of module
BC = 2*AB
BE = AB*tan30
AE = root(AB^2 + BE^2)
EF=EG = 2/5 AE
AF = 3/5 EG
AL = AF*cos30
LF = AF*sin30
BG = BE+EG

Now I can start to get somewhere...

Blender

ArchiCAD mesh

And this was as far as I got!